Studies of Exactly Solvable Models in Statistical Mechanics

这是一个持续的研究项目，用于研究手征POTS或广义手征时钟模型中的许多未解决的问题。特例被引入作为研究无公度状态、润湿和公度-非公度相变的有效模型。当不同层中的分子大小不相容时，这种现象可能发生在表层；生物膜中的波纹态就是一个例子。从数学的角度出发，研究了一类新的循环超几何函数，它们与最近发现的精确解有关。将寻求新的成果，进一步探索数学、物理和其他科学的各个领域之间的联系。新的结构和模型将用分析方法、符号处理和数值技术进一步研究，如蒙特卡罗分析和边界上平均场为有限条上的系统。这应该会导致更好地理解更一般的模型。

This is a continuing research project for the study of many of the unsolved problems in chiral Potts or generalized chiral clock models. Special cases have been introduced as effective models for the study of incommensurate states, wetting, and commensurate-incommensurate phase transitions. Such phenomena can occur in surface layers when the molecules in different layers have incompatible sizes; an example is ripple states in biomembranes. From a mathematical point of view, this research addresses a new class of cyclic hypergeometric functions, related to exact solutions found recently. New results will be pursued and connections between various fields of mathematics, physics, and other sciences will be further explored. New structures and models will be investigated further with analytic means, symbolic manipulation and numerical techniques, such as Monte Carlo analysis and systems on finite strips with mean fields on the boundaries. This should lead to better understanding of more general models.